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Full text of "Analytical Mechanics"

MOTION OF A PARTICLE 115 g must be replaced by (-g) before they are applied to the motion of bodies which are projected vertically upwards. PROBLEMS. 1. A steel plate weighing 10 pounds is placed on a perfectly smooth and perfectly horizontal sheet of ice. The plate is then moved by means of a string, cne end of which is fastened to the plate, and the string is pulled in a direction parallel to the surface of the ice. Is it necessary to apply a force to the string in order to give the plate a desired velocity? Why? What will the magnitude of the force depend upon? 2. In the preceding problem the block is given a velocity of 100 —- sec. in 5 seconds. Find the tension of the string supposing it to be constant. How far will the plate have traveled in the meantime ? 3. In the preceding problem the string is just strong enough to support half the weight of the plate. What is the shortest time in which the plate can be pulled through a distance of 162 feet? 4. In the preceding problem suppose the contact to be rough and to have a coefficient of friction equal to 0.1. 6. A bullet is fired with a muzzle velocity of 500 meters. Find the sec. average acceleration, supposing the length of the barrel to be 80 cm. 6. A stone is sent gliding over a horizontal sheet of ice with a speed of 10 —-i—. How far and how-long will it move if the coefficient of sec. friction is 0.1? 7. An elevator starts from rest and rises to a height of 100 feet in 10 seconds, with a constantly increasing velocity. Find the increase.in pressure exerted on the feet of a man in the elevator who weighs 150 pounds. 8. A man can just lift 350 pounds when on the ground. How much can he lift when in an elevator descending with an acceleration of 4 —-2? sec. 9. An elevator starts from rest and rises 100 feet in five seconds, with a constant acceleration. Find the tension of the rope which pulls it up if the elevator weighs 2000 pounds; neglect the frictional forces. rji 10. A body is projected vertically upward with a velocity of 50 —- at sec. the edge of a pit 200 feet deep. When will it strike the bottom? 11. What is the lowest level, over the enemy's camp, to which a balloon can safely descend, if the enemy is provided with guns which have muzzle velocities of 2000 feet per second?